2619 papers
Mathematical physics sits at the fascinating intersection where abstract equations meet the fundamental laws of our universe. This field uses rigorous mathematical tools to model everything from the behavior of subatomic particles to the curvature of spacetime, turning complex theories into testable predictions. It is the language through which physicists describe reality, bridging the gap between pure mathematics and physical observation.
On Gist.Science, we process every new preprint published in this category on arXiv to make these dense studies accessible to everyone. Whether you are a specialist or a curious reader, you will find both plain-language overviews and detailed technical summaries for each paper. Below are the latest mathematical physics papers from arXiv, curated to help you explore the cutting edge of theoretical science.
This paper establishes an arithmetic analogue of quantum field theory trace-path integral formulae by proving that an arithmetic path integral over the -torsion of a Jacobian equals the trace of the Frobenius action on a Heisenberg group representation, up to a specific sign.
This paper establishes that the topological properties and symmetry-enriched order of bivariate-bicycle codes can be systematically determined by analyzing their prime-factor counterparts, thereby enabling the generalization of algebraic-geometric methods to resolve anyon fusion rules and quasifractonic mobility puzzles in qudit stabilizer codes.
This paper demonstrates that the relativistic energy-momentum relation emerges as an effective ensemble-averaged structure from a multiplicative Hamiltonian under maximum entropy inference, where scale-invariant constraints derived from Fisher-Rao geometry naturally yield the relativistic dispersion relation without initially imposing Lorentz symmetry.
This paper establishes sufficient conditions for the existence of local and global solutions to Wick renormalized stochastic quantization equations with polynomial interactions on rough metric measure spaces exhibiting sub-Gaussian heat kernel behavior, thereby enabling rigorous quantum field theory constructions in non-integer dimensions.
This paper establishes a variational reduction procedure for Lagrangian systems with scaling symmetries, enabling trajectory reconstruction via quadratures and characterizing critical points through scaling-analogous Lagrange-Poincaré equations, while also investigating their relationship with the Herglotz variational principle.
This paper demonstrates that while the spin-1/2 Heisenberg antiferromagnetic chain is integrable, its exact finite-size solutions become algebraically intractable due to Galois unsolvability, with Bethe roots losing analytic solvability at eight sites and ground state properties at ten sites.
This paper rigorously derives the asymptotic free energy and wandering exponents of high-dimensional elastic polymers in continuous Gaussian random environments, establishing a precise correspondence between the transition from diffusive to superdiffusive behavior and the shift from one-step to full-step replica symmetry breaking, thereby confirming key predictions from the physics literature.
This paper investigates the non-relativistic limit of a generalized relativistic Pauli operator on by utilizing a Feynman-Kac representation involving Brownian motion, a subordinator, and a Poisson process to prove the strong convergence of the associated heat semigroup to a limiting generator as the speed of light approaches infinity.
This paper resolves the inherent ambiguity in shock solutions for multi-temperature Euler equations of compressible plasma flows by deriving two distinct, physically admissible Hugoniot relations and demonstrating that microscopic physics, rather than macroscopic PDEs alone, is essential for uniquely determining shock structures.
This contribution presents an algebraic tensor ring decomposition framework that systematically maps nonlinear Yang-Mills equations into tractable differential-algebraic systems and, through the analysis of differential ideal bifurcations and quotient rings, enables the extraction of three distinct classes of exact solutions—including relativistic color waves, dynamic dyonic flux tubes, and configurations.